Answer:
1 13/15 cubic yards more soil
Explanation:
If you say, "I have 3 and I need 5, how many more must I acquire?" you should be able to understand that one formulation of the problem is ...
3 + ___ = 5 . . . . . . what goes in the blank?
You can recognize that the value in the blank is the difference between 3 and 5:
___ = 5 -3 = 2
The same sort of reasoning applies to the given problem, except that now the numbers are mixed numbers that include fractions. Taking the difference involves subtracting mixed numbers, but the idea is fundamentally the same.
5 1/3 + ___ = 7 1/5
___ = 7 1/5 - 5 1/3
= = = = = = = = = = = = = = = = = = =
The subtraction of mixed numbers generally involves (at least) converting the fractions to ones with a common denominator. Here, that denominator will be 5ยท3 = 15, so the problem can be written ...
___ = 7 3/15 -5 5/15
Such a subtraction involves a "rewrite" somewhere along the way. Let's save that to the end, so we have ...
___ = (7 -5) +(3/15 -5/15) = 2 - 2/15
Now we know that 1 = 15/15 so 2 = 1 15/15 and we can rewrite the subtraction as ...
1 15/15 - 2/15 = 1 13/15
Then ...
___ = 7 3/15 - 5 5/15 = 1 13/15
Tierra needs to buy 1 13/15 cubic yards more soil to meet her needs.